The Google map just looks like a grey square with no content in it. I only just noticed this, but I think it began happening after the recent WordPress update. I've tried turning the map option on and off in the plugin's settings page, but that didn't help.

Have you tried deactivating other plugins to look for a conflict, or switching to a default theme like Twenty Twelve? If you can isolate this as an issue that's inherent to The Events Calendar, we'd be happy to look into it further. Unfortunately, we can't help troubleshoot conflicts here on the free forum. If you do find a conflict, you can try getting in touch with the developer of the theme or plugin and see if they can shed some light on the issue.